is of course true only of the surface and sunlit shadows of
the great democratic tide. Its depths conceal every kind of subtlety
and sophistication, high endeavour, and a response to beauty and
wisdom of a sort far removed from the amoeba stage of development
above sketched. Of this latter stage the simple figures of Euclidian
plane and solid geometry--figures which any child can understand--are
the appropriate symbols, but for that other more developed state of
consciousness--less apparent but more important--these will not do.
Something more sophisticated and recondite must be sought for if we
are to have an ornamental mode capable of expressing not only the
simplicity but the complexity of present-day psychology. This need not
be sought for outside the field of geometry, but within it, and by
an extension of the methods already described. There is an altogether
modern development of the science of mathematics: the geometry of
four dimensions. This represents the emancipation of the mind from
the tyranny of mere appearances; the turning of consciousness in a
new direction. It has therefore a high symbolical significance as
typifying that movement away from materialism which is so marked a
phenomenon of the times.

Of course to those whose notion of the fourth dimension is akin to
that of a friend of the author who described it as "a wagon-load
of bung-holes," the idea of getting from it any practical advantage
cannot seem anything but absurd. There is something about this form
of words "the fourth dimension" which seems to produce a sort of
mental-phobia in certain minds, rendering them incapable of perception
or reason. Such people, because they cannot stick their cane into it
contend that the fourth dimension has no mathematical or philosophical
validity. As ignorance on this subject is very general, the following
essay will be devoted to a consideration of the fourth dimension and
its relation to a new ornamental mode.

[Illustration]

II

THE FOURTH DIMENSION

The subject of the fourth dimension is not an easy one to understand.
Fortunately the artist in design does not need to penetrate far into
these fascinating halls of thought in order to reap the advantage
which he seeks. Nevertheless an intention of mind upon this
"fairy-tale of mathematics" cannot fail to enlarge his intellectual
and spiritual horizons, and develop his imagination--that finest
instrument in all his chest of tools.

By way o